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Estimation and Properties of a Time-Varying EGARCH(1,1) in Mean Model

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  • Sofia Anyfantaki

    ()

  • Antonis Demos

    ()
    (www.aueb.gr/users/demos)

Abstract

Time-varying GARCH-M models are commonly employed in econometrics and financial economics. Yet the recursive nature of the conditional variance makes exact likelihood analysis of these models computationally infeasible. This paper outlines the issues and suggests to employ a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a simulated Bayesian solution in only O(T) computational operations, where T is the sample size. Furthermore, the theoretical dynamic properties of a time-varying-parameter EGARCH(1,1)-M are derived. We discuss them and apply the suggested Bayesian estimation to three major stock markets.

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Bibliographic Info

Paper provided by Athens University of Economics and Business in its series DEOS Working Papers with number 1228.

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Date of creation: 30 Jul 2012
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Handle: RePEc:aue:wpaper:1228

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Keywords: Dynamic heteroskedasticity; in mean models; time varying parameter; Markov chain Monte Carlo; simulated EM algorithm; Bayesian inference;

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References

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  1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  2. He, Changli & Ter svirta, Timo & Malmsten, Hans, 2002. "Moment Structure Of A Family Of First-Order Exponential Garch Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 18(04), pages 868-885, August.
  3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
  4. Sentana, Enrique & Fiorentini, Gabriele, 2001. "Identification, estimation and testing of conditionally heteroskedastic factor models," Journal of Econometrics, Elsevier, Elsevier, vol. 102(2), pages 143-164, June.
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  7. Chib, Siddhartha, 1993. "Bayes regression with autoregressive errors : A Gibbs sampling approach," Journal of Econometrics, Elsevier, Elsevier, vol. 58(3), pages 275-294, August.
  8. Vrontos, I D & Dellaportas, P & Politis, D N, 2000. "Full Bayesian Inference for GARCH and EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 18(2), pages 187-98, April.
  9. James M. Poterba & Lawrence H. Summers, 1987. "Mean Reversion in Stock Prices: Evidence and Implications," NBER Working Papers 2343, National Bureau of Economic Research, Inc.
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  11. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1995. "Estimation of Stochastic Volatility Models with Diagnostics," Working Papers, Duke University, Department of Economics 95-36, Duke University, Department of Economics.
  12. Stelios Arvanitis & Antonis Demos, 2004. "Time Dependence and Moments of a Family of Time-Varying Parameter Garch in Mean Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 1-25, 01.
  13. Antonis Demos, 2002. "Moments and dynamic structure of a time-varying parameter stochastic volatility in mean model," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 5(2), pages 345-357, 06.
  14. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, Econometric Society, vol. 57(6), pages 1317-39, November.
  15. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 5-59.
  16. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
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